What does circle symbol between two functions means?

Question

I have two function $f$ and $r$, such that: $y = f(x)$, $r(y) = x$. I read that it means that: $f \circ r = I_{U}$, where $x \in U, y \in U$, where $U$ is a finite set. What does $f \circ r = I_{U}$ mean? What does this circle mean and how could i read all this writing $f \circ r = I_{U}$ ?

Answer 1

The $\circ$ symbol corresponds to the function composition. For any two functions $f:X\to Y$ and $g:Y\to Z$, the new function "$g$ composed with $f$" (denoted by $g\circ f$) is a new function defined as $(g\circ f)(x)=g(f(x))$.

In your case, you have X=Y=Z=U and $g=r$. Then, $I_U=r\circ f$ seems to be the identity function on $U$.